9.03 Tables and arrays
A player is rolling two dice and calculating their sum. They draw a table of all the possible dice rolls for two dice and what they sum to:
Find the probability the dice will sum to 8.
| 1 | 2 | 3 | 4 | 5 | 6 | |
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| 6 | 7 | 8 | 9 | 10 | 11 | 12 |
A player is rolling two dice and calculating their difference, that is the largest number minus the smaller number. They draw a table of all the possible dice rolls for two dice and what their difference is:
List the sample space for the difference of two dice.
What is the probability the dice will have a difference of 0?
| 1 | 2 | 3 | 4 | 5 | 6 | |
|---|---|---|---|---|---|---|
| 1 | 0 | 1 | 2 | 3 | 4 | 5 |
| 2 | 1 | 0 | 1 | 2 | 3 | 4 |
| 3 | 2 | 1 | 0 | 1 | 2 | 3 |
| 4 | 3 | 2 | 1 | 0 | 1 | 2 |
| 5 | 4 | 3 | 2 | 1 | 0 | 1 |
| 6 | 5 | 4 | 3 | 2 | 1 | 0 |
Ben has 3 shirts, each in a different colour: crimson (C), pink (P) and white (W), and 4 ties, each in a different colour: blue (B), grey (G), red (R) and yellow (Y).
How many different combinations are possible?
Find the probability that he is wearing:
A pink shirt and yellow tie.
A pink shirt.
A pink or white shirt.
| C | P | W | |
|---|---|---|---|
| B | C,B | P,B | W,B |
| G | C,G | P,G | G,W |
| R | C,R | P,R | W,R |
| Y | C,Y | P,Y | W,Y |
The following two spinners are spun and the sum of their respective spins are recorded:
Complete the following table to represent all possible combinations:
| \text{Spinner} | 2 | 3 | 4 |
|---|---|---|---|
| 7 | 10 | ||
| 9 | 11 | 13 | |
| 12 | 14 | 16 |
Find the probability that:
The first spinner lands on an even number and the sum is even.
The first spinner lands on a prime number and the sum is odd.
The sum is a multiple of 3.
The following spinner is spun and a normal six-sided die is rolled. The result of each is recorded:
Complete the following table to represent all possible combinations:
| W | X | Y | Z | |
|---|---|---|---|---|
| 1 | 1,\text{W} | 1,⬚ | 1,\text{Y} | 1,\text{Z} |
| 2 | ⬚,\text{W} | 2,\text{X} | 2,\text{Y} | 2,\text{Z} |
| 3 | 3,\text{W} | 3,\text{X} | 3,\text{Y} | ⬚,⬚ |
| 4 | 4,\text{W} | 4,\text{X} | 4,\text{Y} | 4,\text{Z} |
| 5 | 5,\text{W} | 5,\text{X} | ⬚,⬚ | 5,\text{Z} |
| 6 | 6,\text{W} | 6,\text{X} | 6,\text{Y} | 6,\text{Z} |
State the total number of possible outcomes.
Find the probability that:
The spinner lands on X and the dice rolls a prime number.
The spinner lands on W and the dice rolls a factor of 6.
The spinner doesn’t land on Z or the dice doesn't roll a multiple of 3.
The following spinner is spun and a normal six-sided die is rolled. The product of their respective results is recorded.
Construct a table to represent all possible outcomes.
Find the probability of an odd product.
Find the probability of rolling a 5 on the dice and scoring an even product.
Find the probability of spinning a 3 on the spinner or scoring a product which is a multiple of 4.
The following two spinners are spun and the sum of their respective spins is recorded:
Complete the following table to represent all possible outcomes:
| \text{Spinner} | 2 | 4 | 5 |
|---|---|---|---|
| 3 | |||
| 7 |
Find the probability that:
The sum is less than 13.
The sum is odd.
A 7 was spun given that the sum is less than 12.
The sum is odd given that a 4 was spun.
The following two spinners are spun and the result of each spin is recorded:
Complete the table to represent all possible combinations:
State the total number of possible outcomes.
Find the probability that the spinner lands on a consonant and an even number.
Find the probability that the spinner lands on a vowel or a prime number.
| A | B | C | |
|---|---|---|---|
| 1 | 1,A | ||
| 2 | 2,C | ||
| 3 |
Xavier is choosing an outfit for the day and has 3 shirts (cyan, pink, and white) and 4 ties (black, grey, red, and yellow) to select from.
Complete the following table to show all the possible outfits Xavier could wear:
| \text{Cyan }(C) | \text{Pink }(P) | \text{White }(W) | |
|---|---|---|---|
| \text{Black }(B) | C,B | ⬚,B | W,B |
| \text{Grey } (G) | C,G | P,G | W,⬚ |
| \text{Red }(R) | ⬚,⬚ | P,R | W,R |
| \text{Yellow }(Y) | C,Y | ⬚,⬚ | W,Y |
How many different outfits are possible?
What is the probability that he wears a black tie?
What is the probability that he wears a white shirt?
A fair die is rolled twice.
Create a table displaying all possible outcomes.
Find the probability of rolling a:
3 and a 6 in any order.
3 and then a 6.
a double
an odd and an even number
Two spinners labelled 1 to 4 are spun simultaneously and the results added:
Spinner 1
Spinner 2
Construct a table to represent all possible outcomes.
List the sample space for the sum of the two spinners.
Determine the probability of:
An even result.
A result greater than 6.
A result less than 5 and even.
A result less than 5 or even.
A two-digit number is formed by spinning the following two spinners with Spinner 1 being the first digit and Spinner 2 being the second digit in the number:
Spinner 1
Spinner 2
Construct a table to represent all possible outcomes.
Determine the probability the number formed:
Is 25.
Is even.
Is prime.
Is divisible by 5.
Is divisible by 5 and odd.
Contains at least one 2.